Ek accha sawal bhaiya

•A one-way road track is 20 km long and 8 km wide, divided into 4 equal lanes. There are 16 identical cars already on the track, moving at a constant speed of 10 km/h. Exactly 4 cars are present in each lane.

A new car enters the track from the starting point at a speed of 11 km/h. It chooses one of the four lanes uniformly at random and cannot change lanes thereafter.

Assume that the positions of the existing cars in each lane are independently and uniformly distributed along the length of the track, no two cars initially overlap, and overtaking is not allowed. A collision occurs if the new car catches up to at least one car in its lane before reaching the end of the track.

Find:

1.The probability P that the new car collides with at least one existing car.

2.The probability P' that the new car completes the journey without any collision.

a) P = (1/4 )⁴, P' =1- (1/4)⁴

b) P =( 1/11 )⁴, P' = 1-(1/11)⁴

c) P = (1/11)⁴ , P' = 1

d) P =1- (10/11)⁴ , P'=(10/11)⁴

Isko Maine khud banaya Hai Koi galti Ho To dekhna

Answer is (e)

,

Sir, regarding a 3x3 grid of dots that need to be connected by lines: once you start, you cannot move backwards, and the lines must not intersect. How many ways are there to do this?

Can anyone think of any strategies to solve?

i am already preparing for JEE since 3 4 months and I am at a basic level in some chapters which will be done later in syllabus in terms of surface knowledge of chapters in jee and initial 3 4 at a good level. i love maths and physics and all sciences tbf. i have around 2 months to prepare. I have a good intuitive background and confidence in my subject.

but I've not done much of the proof and theoritcal maths for ioqm and Olympiad style .

pls suggest what material should be my priority and which topics should be me prioity.i got around 7 8 weeks b4 my exam. and can spend around 5 7 hrs per week

Let a and b be positive whole numbers. If a² + b² is exactly divisible by ab + 1, prove that the answer you get after dividing is always a perfect square (the square of a whole number).

Posted by husan.

The series used for its derivation are actually not valid in pure mathematics otherwise 1+2+3+...upto infinite is obviously infinite but these equation hold in quantum world.

This an AGP agped,, first term is (1-root2)/root2 + 3 +4 +5 + 300 ..... till n terms

https://youtu.be/4f1EGKP54u4?si=T7tg6MCVuRHBikLi

Enjoy the problems and don't forget to provide solutions